Uncertainty of model parameters in stream pollution using fuzzy arithmetic

Fuzzy arithmetic is employed for the analysis of uncertainties in water-stream pollution, when the various model parameters involved are imprecise. The one-dimensional advection-dispersion equation, for both a conservative and a non-conservative substance, was solved analytically for point and Gaussian-hill input loads of pollution, considering the dispersion and decay coefficients involved as fuzzy numbers. The solution of the advection-dispersion equation was also conducted numerically for the same input loads with the finite-difference method, employing a Lagrangian-Eulerian scheme. The good agreement between analytical and numerical results presented in the form of fuzzy numbers confirms the reliability of the numerical scheme. The advection-dispersion equation of a non-conservative substance was then solved numerically for ten different water quality parameters, in order to study the water pollution in a water stream. The dispersion coefficient, the source terms and the input loads were expressed as fuzzy numbers, and the concentration of each quality parameter was obtained in fuzzy-number form. With fuzzy modeling, imprecise data can be represented and imprecise output produced, with minimal input data requirements and without the need of a large number of computations.